Cinema Problem

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Cinema title image

A cinema has $100$ seats.

Show how it is possible to sell exactly $100$ tickets and take exactly $£100$ if the prices are

$£10$ for adults

$50\text{p}$ for pensioners

$10\text{p}$ for children

Is there only one solution?

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Show that it is also possible to do when the prices change to:

$£10$ for adults

$£1$ for pensioners

$50\text{p}$ for children

How many solutions are there this time?

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This problem is based on Cinema Problem from SIGMA 1 by David Kent and Keith Hedger
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Published October 2003.